Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 23:30:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/15/t147130024399jwnao6ga4lhwb.htm/, Retrieved Sun, 28 Apr 2024 15:41:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 15:41:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
700
700
620
680
700
670
660
730
680
680
650
800
660
710
660
590
660
710
620
700
690
680
640
810
620
700
720
620
630
680
670
720
660
630
620
810
540
690
720
620
650
690
660
700
630
590
570
760
500
660
750
680
710
620
640
720
680
580
530
740
480
640
690
600
640
580
690
690
720
550
510
680
450
560
730
650
680
580
750
670
670
590
480
810
350
570
710
650
710
510
800
680
660
620
580
830
480
550
720
620
730
520
870
660
650
620
560
820





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0128283839087205
beta0.316844895712562
gamma0.882098913021525

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0128283839087205 \tabularnewline
beta & 0.316844895712562 \tabularnewline
gamma & 0.882098913021525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.0128283839087205[/C][/ROW]
[ROW][C]beta[/C][C]0.316844895712562[/C][/ROW]
[ROW][C]gamma[/C][C]0.882098913021525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0128283839087205
beta0.316844895712562
gamma0.882098913021525







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13660665.88141025641-5.88141025641005
14710717.553617412324-7.55361741232377
15660667.090337026059-7.09033702605905
16590595.354180338119-5.35418033811925
17660664.451866424001-4.45186642400074
18710713.1263659808-3.12636598080041
19620651.388495447433-31.3884954474333
20700720.827152205355-20.827152205355
21690666.98330638697123.0166936130295
22680667.96212675755812.0378732424424
23640642.182369174323-2.18236917432284
24810790.79465172030319.2053482796973
25620644.637934204941-24.6379342049414
26700694.4006038967165.59939610328354
27720644.35014195547975.649858044521
28620575.36420030503744.6357996949632
29630646.269062647616-16.269062647616
30680696.278323645305-16.2783236453047
31670610.04022875135859.9597712486421
32720690.49734544274929.502654557251
33660676.332167697489-16.332167697489
34630667.940639809835-37.9406398098355
35620629.628454408439-9.62845440843864
36810797.23047249069512.7695275093049
37540613.248245043084-73.2482450430842
38690688.9549313512541.04506864874588
39720700.06374012090419.936259879096
40620603.34905734700516.6509426529954
41650620.73874177181329.2612582281865
42690671.38782368753318.6121763124668
43660652.1897762393257.81022376067517
44700705.450012320833-5.45001232083303
45630650.775848534148-20.7758485341476
46590623.34454785684-33.3445478568402
47570609.597297040553-39.5972970405534
48760796.049037952508-36.0490379525078
49500536.069696566843-36.069696566843
50660676.629759292872-16.6297592928724
51750703.57319613183746.4268038681626
52680604.0564586755175.9435413244903
53710633.14753390591376.8524660940867
54620675.287448149354-55.2874481493541
55640645.588211835875-5.58821183587543
56720686.92830061155133.0716993884491
57680619.35792725814360.642072741857
58580582.312505948983-2.31250594898302
59530563.930720251335-33.9307202513353
60740753.980112249707-13.9801122497074
61480494.790786212839-14.7907862128391
62640653.163176350586-13.1631763505862
63690735.685144282589-45.6851442825889
64600660.940510505268-60.9405105052676
65640688.761758446251-48.7617584462514
66580613.409178045264-33.4091780452636
67690626.54090679364663.4590932063543
68690701.984856621581-11.9848566215809
69720657.2148577876862.7851422123199
70550564.756426473543-14.7564264735435
71510518.011097294368-8.01109729436826
72680725.199695464181-45.1996954641811
73450464.211104968489-14.2111049684888
74560623.317736124438-63.3177361244376
75730675.98237600505754.0176239949434
76650588.74355757850161.2564424214988
77680628.74503169526651.2549683047342
78580568.45838559267211.5416144073276
79750667.11482764486482.8851723551363
80670677.788454902462-7.78845490246238
81670698.873572364799-28.8735723647987
82590538.03770922486451.9622907751364
83480498.613458733161-18.613458733161
84810673.831219189113136.168780810887
85350443.439195864454-93.4391958644537
86570559.7317720954510.2682279045499
87710716.776670582809-6.77667058280872
88650636.07692632906213.9230736709383
89710667.5852111295642.4147888704401
90510573.39064916353-63.3906491635298
91800733.69322237310766.3067776268925
92680665.61236981786514.3876301821349
93660669.126793892095-9.12679389209472
94620579.52039442125940.4796055787408
95580479.031651697697100.968348302303
96830791.59022663623138.4097733637693
97480360.633065037443119.366934962557
98550571.454912828649-21.4549128286493
99720714.6141547924265.38584520757399
100620653.508565522935-33.5085655229346
101730710.43883350076519.5611664992348
102520524.944980669552-4.94498066955248
103870800.30065364048569.6993463595149
104660688.431820918185-28.4318209181853
105650672.125745513051-22.1257455130507
106620626.700930521409-6.70093052140896
107560579.239667014299-19.2396670142994
108820836.252784586751-16.2527845867514

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 660 & 665.88141025641 & -5.88141025641005 \tabularnewline
14 & 710 & 717.553617412324 & -7.55361741232377 \tabularnewline
15 & 660 & 667.090337026059 & -7.09033702605905 \tabularnewline
16 & 590 & 595.354180338119 & -5.35418033811925 \tabularnewline
17 & 660 & 664.451866424001 & -4.45186642400074 \tabularnewline
18 & 710 & 713.1263659808 & -3.12636598080041 \tabularnewline
19 & 620 & 651.388495447433 & -31.3884954474333 \tabularnewline
20 & 700 & 720.827152205355 & -20.827152205355 \tabularnewline
21 & 690 & 666.983306386971 & 23.0166936130295 \tabularnewline
22 & 680 & 667.962126757558 & 12.0378732424424 \tabularnewline
23 & 640 & 642.182369174323 & -2.18236917432284 \tabularnewline
24 & 810 & 790.794651720303 & 19.2053482796973 \tabularnewline
25 & 620 & 644.637934204941 & -24.6379342049414 \tabularnewline
26 & 700 & 694.400603896716 & 5.59939610328354 \tabularnewline
27 & 720 & 644.350141955479 & 75.649858044521 \tabularnewline
28 & 620 & 575.364200305037 & 44.6357996949632 \tabularnewline
29 & 630 & 646.269062647616 & -16.269062647616 \tabularnewline
30 & 680 & 696.278323645305 & -16.2783236453047 \tabularnewline
31 & 670 & 610.040228751358 & 59.9597712486421 \tabularnewline
32 & 720 & 690.497345442749 & 29.502654557251 \tabularnewline
33 & 660 & 676.332167697489 & -16.332167697489 \tabularnewline
34 & 630 & 667.940639809835 & -37.9406398098355 \tabularnewline
35 & 620 & 629.628454408439 & -9.62845440843864 \tabularnewline
36 & 810 & 797.230472490695 & 12.7695275093049 \tabularnewline
37 & 540 & 613.248245043084 & -73.2482450430842 \tabularnewline
38 & 690 & 688.954931351254 & 1.04506864874588 \tabularnewline
39 & 720 & 700.063740120904 & 19.936259879096 \tabularnewline
40 & 620 & 603.349057347005 & 16.6509426529954 \tabularnewline
41 & 650 & 620.738741771813 & 29.2612582281865 \tabularnewline
42 & 690 & 671.387823687533 & 18.6121763124668 \tabularnewline
43 & 660 & 652.189776239325 & 7.81022376067517 \tabularnewline
44 & 700 & 705.450012320833 & -5.45001232083303 \tabularnewline
45 & 630 & 650.775848534148 & -20.7758485341476 \tabularnewline
46 & 590 & 623.34454785684 & -33.3445478568402 \tabularnewline
47 & 570 & 609.597297040553 & -39.5972970405534 \tabularnewline
48 & 760 & 796.049037952508 & -36.0490379525078 \tabularnewline
49 & 500 & 536.069696566843 & -36.069696566843 \tabularnewline
50 & 660 & 676.629759292872 & -16.6297592928724 \tabularnewline
51 & 750 & 703.573196131837 & 46.4268038681626 \tabularnewline
52 & 680 & 604.05645867551 & 75.9435413244903 \tabularnewline
53 & 710 & 633.147533905913 & 76.8524660940867 \tabularnewline
54 & 620 & 675.287448149354 & -55.2874481493541 \tabularnewline
55 & 640 & 645.588211835875 & -5.58821183587543 \tabularnewline
56 & 720 & 686.928300611551 & 33.0716993884491 \tabularnewline
57 & 680 & 619.357927258143 & 60.642072741857 \tabularnewline
58 & 580 & 582.312505948983 & -2.31250594898302 \tabularnewline
59 & 530 & 563.930720251335 & -33.9307202513353 \tabularnewline
60 & 740 & 753.980112249707 & -13.9801122497074 \tabularnewline
61 & 480 & 494.790786212839 & -14.7907862128391 \tabularnewline
62 & 640 & 653.163176350586 & -13.1631763505862 \tabularnewline
63 & 690 & 735.685144282589 & -45.6851442825889 \tabularnewline
64 & 600 & 660.940510505268 & -60.9405105052676 \tabularnewline
65 & 640 & 688.761758446251 & -48.7617584462514 \tabularnewline
66 & 580 & 613.409178045264 & -33.4091780452636 \tabularnewline
67 & 690 & 626.540906793646 & 63.4590932063543 \tabularnewline
68 & 690 & 701.984856621581 & -11.9848566215809 \tabularnewline
69 & 720 & 657.21485778768 & 62.7851422123199 \tabularnewline
70 & 550 & 564.756426473543 & -14.7564264735435 \tabularnewline
71 & 510 & 518.011097294368 & -8.01109729436826 \tabularnewline
72 & 680 & 725.199695464181 & -45.1996954641811 \tabularnewline
73 & 450 & 464.211104968489 & -14.2111049684888 \tabularnewline
74 & 560 & 623.317736124438 & -63.3177361244376 \tabularnewline
75 & 730 & 675.982376005057 & 54.0176239949434 \tabularnewline
76 & 650 & 588.743557578501 & 61.2564424214988 \tabularnewline
77 & 680 & 628.745031695266 & 51.2549683047342 \tabularnewline
78 & 580 & 568.458385592672 & 11.5416144073276 \tabularnewline
79 & 750 & 667.114827644864 & 82.8851723551363 \tabularnewline
80 & 670 & 677.788454902462 & -7.78845490246238 \tabularnewline
81 & 670 & 698.873572364799 & -28.8735723647987 \tabularnewline
82 & 590 & 538.037709224864 & 51.9622907751364 \tabularnewline
83 & 480 & 498.613458733161 & -18.613458733161 \tabularnewline
84 & 810 & 673.831219189113 & 136.168780810887 \tabularnewline
85 & 350 & 443.439195864454 & -93.4391958644537 \tabularnewline
86 & 570 & 559.73177209545 & 10.2682279045499 \tabularnewline
87 & 710 & 716.776670582809 & -6.77667058280872 \tabularnewline
88 & 650 & 636.076926329062 & 13.9230736709383 \tabularnewline
89 & 710 & 667.58521112956 & 42.4147888704401 \tabularnewline
90 & 510 & 573.39064916353 & -63.3906491635298 \tabularnewline
91 & 800 & 733.693222373107 & 66.3067776268925 \tabularnewline
92 & 680 & 665.612369817865 & 14.3876301821349 \tabularnewline
93 & 660 & 669.126793892095 & -9.12679389209472 \tabularnewline
94 & 620 & 579.520394421259 & 40.4796055787408 \tabularnewline
95 & 580 & 479.031651697697 & 100.968348302303 \tabularnewline
96 & 830 & 791.590226636231 & 38.4097733637693 \tabularnewline
97 & 480 & 360.633065037443 & 119.366934962557 \tabularnewline
98 & 550 & 571.454912828649 & -21.4549128286493 \tabularnewline
99 & 720 & 714.614154792426 & 5.38584520757399 \tabularnewline
100 & 620 & 653.508565522935 & -33.5085655229346 \tabularnewline
101 & 730 & 710.438833500765 & 19.5611664992348 \tabularnewline
102 & 520 & 524.944980669552 & -4.94498066955248 \tabularnewline
103 & 870 & 800.300653640485 & 69.6993463595149 \tabularnewline
104 & 660 & 688.431820918185 & -28.4318209181853 \tabularnewline
105 & 650 & 672.125745513051 & -22.1257455130507 \tabularnewline
106 & 620 & 626.700930521409 & -6.70093052140896 \tabularnewline
107 & 560 & 579.239667014299 & -19.2396670142994 \tabularnewline
108 & 820 & 836.252784586751 & -16.2527845867514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]660[/C][C]665.88141025641[/C][C]-5.88141025641005[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]717.553617412324[/C][C]-7.55361741232377[/C][/ROW]
[ROW][C]15[/C][C]660[/C][C]667.090337026059[/C][C]-7.09033702605905[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]595.354180338119[/C][C]-5.35418033811925[/C][/ROW]
[ROW][C]17[/C][C]660[/C][C]664.451866424001[/C][C]-4.45186642400074[/C][/ROW]
[ROW][C]18[/C][C]710[/C][C]713.1263659808[/C][C]-3.12636598080041[/C][/ROW]
[ROW][C]19[/C][C]620[/C][C]651.388495447433[/C][C]-31.3884954474333[/C][/ROW]
[ROW][C]20[/C][C]700[/C][C]720.827152205355[/C][C]-20.827152205355[/C][/ROW]
[ROW][C]21[/C][C]690[/C][C]666.983306386971[/C][C]23.0166936130295[/C][/ROW]
[ROW][C]22[/C][C]680[/C][C]667.962126757558[/C][C]12.0378732424424[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]642.182369174323[/C][C]-2.18236917432284[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]790.794651720303[/C][C]19.2053482796973[/C][/ROW]
[ROW][C]25[/C][C]620[/C][C]644.637934204941[/C][C]-24.6379342049414[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]694.400603896716[/C][C]5.59939610328354[/C][/ROW]
[ROW][C]27[/C][C]720[/C][C]644.350141955479[/C][C]75.649858044521[/C][/ROW]
[ROW][C]28[/C][C]620[/C][C]575.364200305037[/C][C]44.6357996949632[/C][/ROW]
[ROW][C]29[/C][C]630[/C][C]646.269062647616[/C][C]-16.269062647616[/C][/ROW]
[ROW][C]30[/C][C]680[/C][C]696.278323645305[/C][C]-16.2783236453047[/C][/ROW]
[ROW][C]31[/C][C]670[/C][C]610.040228751358[/C][C]59.9597712486421[/C][/ROW]
[ROW][C]32[/C][C]720[/C][C]690.497345442749[/C][C]29.502654557251[/C][/ROW]
[ROW][C]33[/C][C]660[/C][C]676.332167697489[/C][C]-16.332167697489[/C][/ROW]
[ROW][C]34[/C][C]630[/C][C]667.940639809835[/C][C]-37.9406398098355[/C][/ROW]
[ROW][C]35[/C][C]620[/C][C]629.628454408439[/C][C]-9.62845440843864[/C][/ROW]
[ROW][C]36[/C][C]810[/C][C]797.230472490695[/C][C]12.7695275093049[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]613.248245043084[/C][C]-73.2482450430842[/C][/ROW]
[ROW][C]38[/C][C]690[/C][C]688.954931351254[/C][C]1.04506864874588[/C][/ROW]
[ROW][C]39[/C][C]720[/C][C]700.063740120904[/C][C]19.936259879096[/C][/ROW]
[ROW][C]40[/C][C]620[/C][C]603.349057347005[/C][C]16.6509426529954[/C][/ROW]
[ROW][C]41[/C][C]650[/C][C]620.738741771813[/C][C]29.2612582281865[/C][/ROW]
[ROW][C]42[/C][C]690[/C][C]671.387823687533[/C][C]18.6121763124668[/C][/ROW]
[ROW][C]43[/C][C]660[/C][C]652.189776239325[/C][C]7.81022376067517[/C][/ROW]
[ROW][C]44[/C][C]700[/C][C]705.450012320833[/C][C]-5.45001232083303[/C][/ROW]
[ROW][C]45[/C][C]630[/C][C]650.775848534148[/C][C]-20.7758485341476[/C][/ROW]
[ROW][C]46[/C][C]590[/C][C]623.34454785684[/C][C]-33.3445478568402[/C][/ROW]
[ROW][C]47[/C][C]570[/C][C]609.597297040553[/C][C]-39.5972970405534[/C][/ROW]
[ROW][C]48[/C][C]760[/C][C]796.049037952508[/C][C]-36.0490379525078[/C][/ROW]
[ROW][C]49[/C][C]500[/C][C]536.069696566843[/C][C]-36.069696566843[/C][/ROW]
[ROW][C]50[/C][C]660[/C][C]676.629759292872[/C][C]-16.6297592928724[/C][/ROW]
[ROW][C]51[/C][C]750[/C][C]703.573196131837[/C][C]46.4268038681626[/C][/ROW]
[ROW][C]52[/C][C]680[/C][C]604.05645867551[/C][C]75.9435413244903[/C][/ROW]
[ROW][C]53[/C][C]710[/C][C]633.147533905913[/C][C]76.8524660940867[/C][/ROW]
[ROW][C]54[/C][C]620[/C][C]675.287448149354[/C][C]-55.2874481493541[/C][/ROW]
[ROW][C]55[/C][C]640[/C][C]645.588211835875[/C][C]-5.58821183587543[/C][/ROW]
[ROW][C]56[/C][C]720[/C][C]686.928300611551[/C][C]33.0716993884491[/C][/ROW]
[ROW][C]57[/C][C]680[/C][C]619.357927258143[/C][C]60.642072741857[/C][/ROW]
[ROW][C]58[/C][C]580[/C][C]582.312505948983[/C][C]-2.31250594898302[/C][/ROW]
[ROW][C]59[/C][C]530[/C][C]563.930720251335[/C][C]-33.9307202513353[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]753.980112249707[/C][C]-13.9801122497074[/C][/ROW]
[ROW][C]61[/C][C]480[/C][C]494.790786212839[/C][C]-14.7907862128391[/C][/ROW]
[ROW][C]62[/C][C]640[/C][C]653.163176350586[/C][C]-13.1631763505862[/C][/ROW]
[ROW][C]63[/C][C]690[/C][C]735.685144282589[/C][C]-45.6851442825889[/C][/ROW]
[ROW][C]64[/C][C]600[/C][C]660.940510505268[/C][C]-60.9405105052676[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]688.761758446251[/C][C]-48.7617584462514[/C][/ROW]
[ROW][C]66[/C][C]580[/C][C]613.409178045264[/C][C]-33.4091780452636[/C][/ROW]
[ROW][C]67[/C][C]690[/C][C]626.540906793646[/C][C]63.4590932063543[/C][/ROW]
[ROW][C]68[/C][C]690[/C][C]701.984856621581[/C][C]-11.9848566215809[/C][/ROW]
[ROW][C]69[/C][C]720[/C][C]657.21485778768[/C][C]62.7851422123199[/C][/ROW]
[ROW][C]70[/C][C]550[/C][C]564.756426473543[/C][C]-14.7564264735435[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]518.011097294368[/C][C]-8.01109729436826[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]725.199695464181[/C][C]-45.1996954641811[/C][/ROW]
[ROW][C]73[/C][C]450[/C][C]464.211104968489[/C][C]-14.2111049684888[/C][/ROW]
[ROW][C]74[/C][C]560[/C][C]623.317736124438[/C][C]-63.3177361244376[/C][/ROW]
[ROW][C]75[/C][C]730[/C][C]675.982376005057[/C][C]54.0176239949434[/C][/ROW]
[ROW][C]76[/C][C]650[/C][C]588.743557578501[/C][C]61.2564424214988[/C][/ROW]
[ROW][C]77[/C][C]680[/C][C]628.745031695266[/C][C]51.2549683047342[/C][/ROW]
[ROW][C]78[/C][C]580[/C][C]568.458385592672[/C][C]11.5416144073276[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]667.114827644864[/C][C]82.8851723551363[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]677.788454902462[/C][C]-7.78845490246238[/C][/ROW]
[ROW][C]81[/C][C]670[/C][C]698.873572364799[/C][C]-28.8735723647987[/C][/ROW]
[ROW][C]82[/C][C]590[/C][C]538.037709224864[/C][C]51.9622907751364[/C][/ROW]
[ROW][C]83[/C][C]480[/C][C]498.613458733161[/C][C]-18.613458733161[/C][/ROW]
[ROW][C]84[/C][C]810[/C][C]673.831219189113[/C][C]136.168780810887[/C][/ROW]
[ROW][C]85[/C][C]350[/C][C]443.439195864454[/C][C]-93.4391958644537[/C][/ROW]
[ROW][C]86[/C][C]570[/C][C]559.73177209545[/C][C]10.2682279045499[/C][/ROW]
[ROW][C]87[/C][C]710[/C][C]716.776670582809[/C][C]-6.77667058280872[/C][/ROW]
[ROW][C]88[/C][C]650[/C][C]636.076926329062[/C][C]13.9230736709383[/C][/ROW]
[ROW][C]89[/C][C]710[/C][C]667.58521112956[/C][C]42.4147888704401[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]573.39064916353[/C][C]-63.3906491635298[/C][/ROW]
[ROW][C]91[/C][C]800[/C][C]733.693222373107[/C][C]66.3067776268925[/C][/ROW]
[ROW][C]92[/C][C]680[/C][C]665.612369817865[/C][C]14.3876301821349[/C][/ROW]
[ROW][C]93[/C][C]660[/C][C]669.126793892095[/C][C]-9.12679389209472[/C][/ROW]
[ROW][C]94[/C][C]620[/C][C]579.520394421259[/C][C]40.4796055787408[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]479.031651697697[/C][C]100.968348302303[/C][/ROW]
[ROW][C]96[/C][C]830[/C][C]791.590226636231[/C][C]38.4097733637693[/C][/ROW]
[ROW][C]97[/C][C]480[/C][C]360.633065037443[/C][C]119.366934962557[/C][/ROW]
[ROW][C]98[/C][C]550[/C][C]571.454912828649[/C][C]-21.4549128286493[/C][/ROW]
[ROW][C]99[/C][C]720[/C][C]714.614154792426[/C][C]5.38584520757399[/C][/ROW]
[ROW][C]100[/C][C]620[/C][C]653.508565522935[/C][C]-33.5085655229346[/C][/ROW]
[ROW][C]101[/C][C]730[/C][C]710.438833500765[/C][C]19.5611664992348[/C][/ROW]
[ROW][C]102[/C][C]520[/C][C]524.944980669552[/C][C]-4.94498066955248[/C][/ROW]
[ROW][C]103[/C][C]870[/C][C]800.300653640485[/C][C]69.6993463595149[/C][/ROW]
[ROW][C]104[/C][C]660[/C][C]688.431820918185[/C][C]-28.4318209181853[/C][/ROW]
[ROW][C]105[/C][C]650[/C][C]672.125745513051[/C][C]-22.1257455130507[/C][/ROW]
[ROW][C]106[/C][C]620[/C][C]626.700930521409[/C][C]-6.70093052140896[/C][/ROW]
[ROW][C]107[/C][C]560[/C][C]579.239667014299[/C][C]-19.2396670142994[/C][/ROW]
[ROW][C]108[/C][C]820[/C][C]836.252784586751[/C][C]-16.2527845867514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13660665.88141025641-5.88141025641005
14710717.553617412324-7.55361741232377
15660667.090337026059-7.09033702605905
16590595.354180338119-5.35418033811925
17660664.451866424001-4.45186642400074
18710713.1263659808-3.12636598080041
19620651.388495447433-31.3884954474333
20700720.827152205355-20.827152205355
21690666.98330638697123.0166936130295
22680667.96212675755812.0378732424424
23640642.182369174323-2.18236917432284
24810790.79465172030319.2053482796973
25620644.637934204941-24.6379342049414
26700694.4006038967165.59939610328354
27720644.35014195547975.649858044521
28620575.36420030503744.6357996949632
29630646.269062647616-16.269062647616
30680696.278323645305-16.2783236453047
31670610.04022875135859.9597712486421
32720690.49734544274929.502654557251
33660676.332167697489-16.332167697489
34630667.940639809835-37.9406398098355
35620629.628454408439-9.62845440843864
36810797.23047249069512.7695275093049
37540613.248245043084-73.2482450430842
38690688.9549313512541.04506864874588
39720700.06374012090419.936259879096
40620603.34905734700516.6509426529954
41650620.73874177181329.2612582281865
42690671.38782368753318.6121763124668
43660652.1897762393257.81022376067517
44700705.450012320833-5.45001232083303
45630650.775848534148-20.7758485341476
46590623.34454785684-33.3445478568402
47570609.597297040553-39.5972970405534
48760796.049037952508-36.0490379525078
49500536.069696566843-36.069696566843
50660676.629759292872-16.6297592928724
51750703.57319613183746.4268038681626
52680604.0564586755175.9435413244903
53710633.14753390591376.8524660940867
54620675.287448149354-55.2874481493541
55640645.588211835875-5.58821183587543
56720686.92830061155133.0716993884491
57680619.35792725814360.642072741857
58580582.312505948983-2.31250594898302
59530563.930720251335-33.9307202513353
60740753.980112249707-13.9801122497074
61480494.790786212839-14.7907862128391
62640653.163176350586-13.1631763505862
63690735.685144282589-45.6851442825889
64600660.940510505268-60.9405105052676
65640688.761758446251-48.7617584462514
66580613.409178045264-33.4091780452636
67690626.54090679364663.4590932063543
68690701.984856621581-11.9848566215809
69720657.2148577876862.7851422123199
70550564.756426473543-14.7564264735435
71510518.011097294368-8.01109729436826
72680725.199695464181-45.1996954641811
73450464.211104968489-14.2111049684888
74560623.317736124438-63.3177361244376
75730675.98237600505754.0176239949434
76650588.74355757850161.2564424214988
77680628.74503169526651.2549683047342
78580568.45838559267211.5416144073276
79750667.11482764486482.8851723551363
80670677.788454902462-7.78845490246238
81670698.873572364799-28.8735723647987
82590538.03770922486451.9622907751364
83480498.613458733161-18.613458733161
84810673.831219189113136.168780810887
85350443.439195864454-93.4391958644537
86570559.7317720954510.2682279045499
87710716.776670582809-6.77667058280872
88650636.07692632906213.9230736709383
89710667.5852111295642.4147888704401
90510573.39064916353-63.3906491635298
91800733.69322237310766.3067776268925
92680665.61236981786514.3876301821349
93660669.126793892095-9.12679389209472
94620579.52039442125940.4796055787408
95580479.031651697697100.968348302303
96830791.59022663623138.4097733637693
97480360.633065037443119.366934962557
98550571.454912828649-21.4549128286493
99720714.6141547924265.38584520757399
100620653.508565522935-33.5085655229346
101730710.43883350076519.5611664992348
102520524.944980669552-4.94498066955248
103870800.30065364048569.6993463595149
104660688.431820918185-28.4318209181853
105650672.125745513051-22.1257455130507
106620626.700930521409-6.70093052140896
107560579.239667014299-19.2396670142994
108820836.252784586751-16.2527845867514







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109475.339891019615392.100117748809558.579664290422
110561.76938121443478.517731591697645.021030837164
111728.427736603863645.157811267063811.697661940662
112633.213977772237549.918007280522716.509948263953
113736.752040796986653.420889283878820.083192310094
114529.553918095238446.177088300985612.930747889491
115869.878343184765786.443983079429953.3127032901
116671.287431075461587.782342276312754.79251987461
117660.575881265553576.985529442194744.166233088912
118628.695071094421545.003598542574712.386543646268
119570.256988096372486.447228646192654.066747546551
120830.05178477527746.105281182407913.998288368132

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 475.339891019615 & 392.100117748809 & 558.579664290422 \tabularnewline
110 & 561.76938121443 & 478.517731591697 & 645.021030837164 \tabularnewline
111 & 728.427736603863 & 645.157811267063 & 811.697661940662 \tabularnewline
112 & 633.213977772237 & 549.918007280522 & 716.509948263953 \tabularnewline
113 & 736.752040796986 & 653.420889283878 & 820.083192310094 \tabularnewline
114 & 529.553918095238 & 446.177088300985 & 612.930747889491 \tabularnewline
115 & 869.878343184765 & 786.443983079429 & 953.3127032901 \tabularnewline
116 & 671.287431075461 & 587.782342276312 & 754.79251987461 \tabularnewline
117 & 660.575881265553 & 576.985529442194 & 744.166233088912 \tabularnewline
118 & 628.695071094421 & 545.003598542574 & 712.386543646268 \tabularnewline
119 & 570.256988096372 & 486.447228646192 & 654.066747546551 \tabularnewline
120 & 830.05178477527 & 746.105281182407 & 913.998288368132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]475.339891019615[/C][C]392.100117748809[/C][C]558.579664290422[/C][/ROW]
[ROW][C]110[/C][C]561.76938121443[/C][C]478.517731591697[/C][C]645.021030837164[/C][/ROW]
[ROW][C]111[/C][C]728.427736603863[/C][C]645.157811267063[/C][C]811.697661940662[/C][/ROW]
[ROW][C]112[/C][C]633.213977772237[/C][C]549.918007280522[/C][C]716.509948263953[/C][/ROW]
[ROW][C]113[/C][C]736.752040796986[/C][C]653.420889283878[/C][C]820.083192310094[/C][/ROW]
[ROW][C]114[/C][C]529.553918095238[/C][C]446.177088300985[/C][C]612.930747889491[/C][/ROW]
[ROW][C]115[/C][C]869.878343184765[/C][C]786.443983079429[/C][C]953.3127032901[/C][/ROW]
[ROW][C]116[/C][C]671.287431075461[/C][C]587.782342276312[/C][C]754.79251987461[/C][/ROW]
[ROW][C]117[/C][C]660.575881265553[/C][C]576.985529442194[/C][C]744.166233088912[/C][/ROW]
[ROW][C]118[/C][C]628.695071094421[/C][C]545.003598542574[/C][C]712.386543646268[/C][/ROW]
[ROW][C]119[/C][C]570.256988096372[/C][C]486.447228646192[/C][C]654.066747546551[/C][/ROW]
[ROW][C]120[/C][C]830.05178477527[/C][C]746.105281182407[/C][C]913.998288368132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109475.339891019615392.100117748809558.579664290422
110561.76938121443478.517731591697645.021030837164
111728.427736603863645.157811267063811.697661940662
112633.213977772237549.918007280522716.509948263953
113736.752040796986653.420889283878820.083192310094
114529.553918095238446.177088300985612.930747889491
115869.878343184765786.443983079429953.3127032901
116671.287431075461587.782342276312754.79251987461
117660.575881265553576.985529442194744.166233088912
118628.695071094421545.003598542574712.386543646268
119570.256988096372486.447228646192654.066747546551
120830.05178477527746.105281182407913.998288368132



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')